Structural and dynamical properties of supercritical fluids are expected to depend smoothly on temperature and pressure. Recently it was suggested to analyze the propagating density fluctuations in supercritical fluids as a function of pressure/density, based on the idea that dynamical properties could be more sensitive to phase changes than the structural properties. Using a combination of inelastic X-ray scattering experiments and molecular dynamics (MD) simulations, it was discovered [1,2] that the onset of deviation from the hydrodynamic dispersion of sound (the so-called “positive sound dispersion” (PSD)) could be used as a boundary between liquid-like and gas-like regions existing in a fluid as reminiscent of the subcritical behavior.We present a theory of PSD in fluids based on thermo-viscoelastic model of generalized hydrodynamics [3]. The developed theory allows to recover density/pressure dependence of PSD observed in X-ray scattering experiments [1] and simulations[2,3]. The analysis of different contributions to PSD reveals that the contribution from heat processes reduces the PSD and when getting closer to the critical point it can result in even "negative sound dispersion".A comparison of the developed theory with another approach to the dynamics of supercritical fluids connected with so-called "Frenkel line" will be discussed [4]. In particular, the dispersion of longitudinal and transverse collective excitations will be compared as obtained from the two theoretical approaches.[1] Simeoni, G.; Bryk, T.; Gorelli, F. A.; Krisch, M.; Ruocco, G.; Santoro, M.; Scopigno, T. Nat. Phys. vol.6, p.503 (2010).[2] Gorelli, F. A.; Bryk, T.; Krisch, M.; Ruocco, G.; Santoro, M.; Scopigno, T. Sci. Rep. vol. 3, 1203 (2013).[3] Bryk, T., Mryglod, I., Scopigno, T., Ruocco, G., Gorelli, F., Santoro, M. J.Chem. Phys. vol.133, 024502 (2010)[4] Bryk, T., Gorelli, F., Mryglod, I., Ruocco, G., Santoro, M., Scopigno, T. J.Phys.Chem. Lett. vol.8, p.4995 (2017)